Question: Which of the following ordered pairs represents a solution to the equation below? $(-2, 6) (-1, 3) (0, 3) (1, -3) (2, -1)$ $y = -2x+1$
Solution: We can try plugging in the x-value of each ordered pair into the equation. If we evaluate and get the y-value of the ordered pair, then that ordered pair is a solution! Let's consider $(-2, 6)$ If we plug in $-2$ for $x$ and evaluate, do we get $6$ $y = (-2)(-2) + 1 = 4 + 1 = 5$ Let's consider $(-1, 3)$ If we plug in $-1$ for $x$ and evaluate, do we get $3$ $y = (-2)(-1) + 1 = 2 + 1 = 3$ Let's consider $(0, 3)$ If we plug in $0$ for $x$ and evaluate, do we get $3$ $y = (-2)(0) + 1 = 0 + 1 = 1$ Let's consider $(1, -3)$ If we plug in $1$ for $x$ and evaluate, do we get $-3$ $y = (-2)(1) + 1 = -2 + 1 = -1$ Let's consider $(2, -1)$ If we plug in $2$ for $x$ and evaluate, do we get $-1$ $y = (-2)(2) + 1 = -4 + 1 = -3$ Thus the only ordered pair that is a solution to the equation is $(-1, 3)$ We come to the same answer by plotting the points and the equation. $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$ $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$